Efficient evolutionary algorithm for the vehicle routing problem with time windows: edge assembly crossover for the VRPTW

We propose an evolutionary algorithm (EA) for the vehicle routing problem with time windows (VRPTW). In particular, a crossover operator suitable for solving the VRPTW are presented. The proposed crossover is designed by extending edge assembly crossover (EAX) which was originally designed for the traveling salesman problem (TSP). Moreover, we propose an efficient modification procedure to eliminate violations of the capacity constraints and the time window constraints because intermediate solutions generated by EAX violate these constraints. The EA is composed of EAX, the modification procedure and a very simple local search. The EA is applied to the well-known Gering and Homberger benchmarks for the VRPTW. The EA finds new best-known solutions in 119 of the 180 instances (200 - 600 customer benchmarks).